Minimum sample sizes required for post-epidemic seroepidemiological studies of final size as a function of the margin error, the reproduction number, and the coefficient of variation of the generation time.

<p>(A & B) Sample size with three different reproduction numbers as a function of the margin of error. (A) employs an estimation formula based Type I error alone (at <i>α</i> = 0.05), while (B) accounts for both Type I and II errors (at <i>α</i> = 0.05 and 1−<i>β</i> = 0.80). The margin of error represents random sampling error, around which the reported percentage would include the true percentage. Since (A) is a special case of (B) (with <i>β</i> = 0.50), <i>R</i> = 1.40 in (A) is also shown as dotted line in (B). The coefficient of variation (CV) of the generation time and the proportion of population with pre-existing immunity are fixed at 40.7% and 7.5%, respectively. (C & D) Sample size with three different coefficients of variation as a function of the margin of error. (C) accounts for Type I error alone (<i>α</i> = 0.05), while (D) accounts for both Type I and II errors (<i>α</i> = 0.05 and 1−<i>β</i> = 0.80). The reproduction number and the proportion of population with pre-existing immunity are fixed at 1.40 and 7.5%, respectively. CV = 0 corresponds to a constant generation time, whereas CV = 1 represents an exponentially distributed generation time. In (B) and (D), several lines are truncated, due to impossibility to account for larger margins of error in the estimation formula.